Question

If m is the slope of a common tangent to the curves
$\frac{x²}{16} + \frac{y²} {9} = 1$
and x 2 + y 2 = 12, then 12 m 2 is equal to:

• A. 6
• B. 9
• C. 10
• D. 12

Answer 1

Answer: (B)

9

Answer 2

The correct answer is (B) : 9
$C1 : \frac{x²}{16} + \frac{y²}{9} = 1$
and
$C2 : x² + y² = 12$
Let
$y = mx ± \sqrt{16m² + 9}$
be any tangent to C1 and if this is also tangent to C2 then
$|\frac{ \sqrt{16m² + 9}}{\sqrt{m² + 1 }}| = √12$
$⇒ 16m² + 9 = 12m² + 12$
$⇒ 4m² = 3 ⇒ 12m² = 9$